Question: Solve for $x$ and $y$ using elimination. ${-3x-2y = -41}$ ${5x+2y = 55}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-3x-2y = -41}\thinspace$ to find $y$ ${-3}{(7)}{ - 2y = -41}$ $-21-2y = -41$ $-21{+21} - 2y = -41{+21}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {5x+2y = 55}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ + 2y = 55}$ ${y = 10}$